Filtrations on block subalgebras of reduced enveloping algebras

Ionov Andrei; Pentland Dylan

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Filtrations on block subalgebras of reduced enveloping algebras

机译：Filtrations on block subalgebras of reduced enveloping algebras

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We study the interaction between the block decompositions of reduced enveloping algebras in positive characteristic, the Poincaré-Birkhoff-Witt (PBW) filtration, and the nilpotent cone. We provide two natural versions of the PBW filtration on the block subalgebra Aλ of the restricted universal enveloping algebra ?χ(?) and show these are dual to each other. We also consider a shifted PBW filtration for which we relate the associated graded algebra to the algebra of functions on the Frobenius neighborhood of 0 in the nilpotent cone and the coinvariants algebra corresponding to λ. In the case of ?=??2(k) in characteristic p>2 we determine the associated graded algebras of these filtrations on block subalgebras of ?0(??2). We also apply this to determine the structure of the adjoint representation of ?0(??2).

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来源
《Journal of algebra and its applications》 |2022年第12期|共32页
作者
Ionov Andrei; Pentland Dylan;
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作者单位

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139,USA;

Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139,USA;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
PBW filtration; reduced universal enveloping algebra; modular representation theory; blocks of representations;

Filtrations on block subalgebras of reduced enveloping algebras

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